The conjugate of a product of linear relations

summary:Let $X$, $Y$ and $Z$ be normed linear spaces with $T(X\rightarrow Y)$ and $S(Y\rightarrow Z)$ linear relations, i.e. setvalued maps. We seek necessary and sufficient conditions that would ensure that $(ST)'=T'S'$. First, we cast the concepts of relative boundedness and co-continuity in the set valued case and establish a duality. This duality turns out to be similar to the one that exists for densely defined linear operators and is then used to establish the necessary and sufficient conditions. These conditions are similar to those for the single valued case. In the process, the well known characterisation of relativeboundedness for closed linear operators by Sz.-Nagy is extended to the multivalued linear maps and we compare our results to other known necessary and sufficient conditions

Adjusting pedagogy to optimise negotiability and interactivity in lessons using the interactive whiteboard an action research study in a primary school

Includes bibliographical references.One of the recent technological devices that have been introduced in the educational domain is the interactive whiteboard (IWB). IWBs have become established teaching and learning tools, particularly in primary school classrooms in developed English speaking countries and have more recently been deployed in developing countries such as South Africa. The Western Cape Province in South Africa has rolled out a province-wide IWB programme over the last decade, despite limited local research on the pedagogical value of IWBs in South African schools. This research study aims to investigate how the IWB can be used to encourage collaboration amongst the learners in a Grade 6 Technology Education class at a primary school in the Western Cape and specifically to assist the teacher in understanding how her pedagogy needs to change to optimise learner collaboration in association with an IWB. To understand the ways in which the IWB influences the activities in the classroom, Activity Theory is used as a framework to understand the tensions that arise and how the teacher needs to change her pedagogical strategies to successfully resolve these tensions

Mathematical Literacy of Students in First Year of Medical School at a South African University

The literature pertaining to the definition of Mathematical Literacy (particularly in the Tertiary context) is briefly reviewed. A Mathematical Literacy questionnaire, designed in accordance with this definition, was administered to students entering the MBChB Program at a South African university in 2003. In general the level of Mathematical Literacy of Medical students is higher than that of entry-level Humanities students, and comparable with that of Science students doing Earth or Biological sciences. The response to the results of this testing, in terms of curriculum interventions in the first year of MBChB, are outlined and their degree of success is evaluated. The post-testing of the MBChB students indicated a statistically significant increase in the Mathematical Literacy of these students

My home — the hospital: A case study

The first years of life, so important in a child’s development, should be spent with its mother in a normal family environment. If the child is denied this, then permanent emotional and intellectual disability can result. This article describes how we tried to prevent this from occurring in Andrew, a little boy who had to spend the first three years of his life in hospital because of a tracheostomy. Hopefully, this account will help others who deal with chronically hospitalised children to anticipate some of the problems that can arise and give them an insight into the vital role of the nurse in dealing with the situation

Perceptions of Powerlessness Are Negatively Associated with Taking Action on Climate Change: A Preregistered Replication

“Final publication is available from Mary Ann Liebert, Inc., publishers https://www.liebertpub.com/doi/10.1089/eco.2020.0012]”Despite segments of skepticism, the majority of the general public in most countries believe that climate change is occurring and caused by human activities. Behavior changes by individuals can reduce greenhouse gas emissions to at least some extent, but a range of psychological and economic barriers can prevent individuals from taking action. A survey of New Zealanders by Aitken, Chapman, and McClure (2011) reported that belief in human influence on climate change and the risks of climate change were positively correlated with taking action on climate change. Conversely, perceptions of powerlessness and the commons dilemma were negatively correlated with taking action on climate change. Feeling powerless was associated with placing less importance on climate change as an influence on actions. Although the study by Aitken et al. has been influential, it was exploratory in nature, had a moderate sample size, was not preregistered, and has not previously been replicated. In this study, we report a preregistered replication with a sample of 352 Australians testing four hypotheses based on Aitken et al.'s findings (as summarized above). All four hypotheses were supported, reproducing Aitken et al.'s key findingsfals

An investigation into whether a leadership and management development project changed the perceptions of the educators in a black, disadvantaged school

This study investigates whether a leadership and management development programme changed the management perceptions of the teachers of one of the schools that participated in the programme. The programme seeks to change the organisational culture of schools and develop effective management. The development philosophy of the programme is informed by literature on school effectiveness, organisation development, whole school development and systemic change. My research is conducted in the interpretive paradigm. Interpretive researchers view reality a construct of the human mind, and therefore the way people perceive the world is not necessarily the same since there can be different understandings of what is real. I employ convenience sampling to select the school and purposive sampling to identify my research participants. Whilst overall impression that the data conveys is that much of the programme does not seem to have had a lasting effect on the culture of the school, it nonetheless made an impression on the teachers’ perceptions of management. There clearly seems to be a greater appreciation of participative management processes. The reintroduction of proper prior planning played a decisive role in re-establishing sound work ethics at the school and contributes to a more structured approach to events at the school. Some sort of organisational learning has also been introduced at the school. The realisation on the part of the staff that they now have their destiny in their own hands is an especially critical development. And whilst the vision is not a compelling force in the organisation, it has nevertheless produced some strategic focus at the school. The insights and skills they acquired concerning resource management will also stand them in good stead

Exploring undergraduate students’ productive struggles in a quantitative literacy course: Implications for the development of tutoring

The present study explores undergraduate students’ productive struggles in a Quantitative Literacy (QL) course, when doing exercises on the statistical concept of confidence intervals (CIs) within the context of odds ratios (ORs), embedded in everyday authentic contexts. The research methodology employed in this study is lesson study, in which tutors and researchers work together to plan the research tutorial, observe and teach it, and reflect on the instruction in general within the research tutorial. Data for this study comprises video- and audio- recorded transcriptions of the observation and teaching, and reflections of tutors on research tutorials. In addition, samples of students’ work and their achievements in assessments were analysed. Results from the study showed that the students’ struggles were initiated when their prior knowledge was not sufficient for them to understand the concept of CIs in relation to ORs. The results also highlight some of the ways in which tutors can notice and address students’ productive struggles during tutorials. Future researchers should focus on identifying which instructional approaches can promote and support prolific productive struggles for students during tutoring

Participatory parity through teaching with Telegram

The COVID19 pandemic thrust emergency remote teaching (ERT) into the global spotlight and thereby undeniably changed aspects of the higher education (HE) landscape. For a developing country such as South Africa (SA), the use of the mobile instant messaging (MIM) application (app) called Telegram represents a practicable solution to overcome historical socio-economic challenges faced by certain demographic groups of limited or restricted access to devices and data. Against this backdrop, a Telegram teaching intervention was developed by two lecturers in the Engineering Faculty at a University of Technology (UoT) in SA to deliver curriculum content and engage with students in a low-tech, low-cost/low-data usage manner, and consequently to widen access to education, promote inclusivity and thereby facilitate student access, retention and success. This study explored student perceptions of the MIM app being used as a primary vehicle to deliver succinct instructional materials and facilitate class activities to offset the lack of faceto-face classes in a multimodal and flexible curriculum delivery approach. Following the completion of the Telegram teaching intervention, a mixed method approach was used that included two online surveys measuring different aspects of the same project (n=34 and n=32) and a focus group interview (n=6). Three research lenses suggested by Fraser (2008) were used to evaluate student perceptions of the usefulness and (dis)advantages of Telegram. These lenses were: (1) redistribution (of resources), (2) recognition (related to social status) and (3) representation (who can act/say/ challenge in an academic environment). Ethical clearance was obtained from Cape Peninsula University of Technology’s Ethics committee. Initial results indicate that using the Telegram app for teaching and learning was successful. Significantly, the app allows for the emergence of a socially just online classroom environment and an inclusive and enabling learning experience for the students during a very disruptive and fearful time in the world’s history

The relationship between reasons for living and suicidal ideation : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Psychology at Massey University, Auckland, New Zealand

Suicide and suicide-related behaviours are widely acknowledged as a major public health issue and the acute nature of suicidal behaviour makes it significant in human consciousness. However, the various causes of suicidal thoughts and behaviour are convoluted and not fully understood. Recommendations stemming from research advocate for a better understanding of the suicidal process, specifically suicidal ideation, as this could enhance efforts in the reduction and impact of suicidal behaviour. Research has shown that Reasons for Living explains variance in suicidal ideation that is not explained by recognised risk factors. The aim of this study was therefore to augment our understanding of suicidal ideation in terms of the extent to which reasons for living predicts suicidal ideation after accounting for specific risk factors: depression, hopelessness, thwarted belongness and perceived burdensomeness. This study also sought to explore the extent to which reasons for living potentially moderates the effects of depression on suicidal ideation. Data was gathered via an anonymous online survey questionnaire in a convenience sample of 577 Australian and New Zealand adults. Hierarchal multiple regression models estimated using ordinary least squares were used to determine whether reasons for living was a significant negative predictor of suicidal ideation, and whether the relationship between depression and suicidal ideation is weaker for people with more reasons for living, while controlling for depression, hopelessness, perceived burdensomeness and thwarted belongingness. Results show that reasons for living is a significant negative predictor of suicidal ideation. The results also show that depression predicts higher suicide ideation, and this effect is moderated by reason for living. Structural Equation Modelling (SEM) was applied, with all study variables treated as latent to allow for the effects of measurement error to be explicitly modelled and accounted for. Results showed that although the SEM model was not considered a good fit to the data, the coefficients across the SEM and OLS techniques were comparable. Both models found reasons for living, depression and perceived burdensomeness to be significant predictors of suicidal ideation. The findings of this research could have meaningful clinical relevance in the assessment and evaluation of suicide risk. Specifically, identifying variations in suicidal ideation via reasons for living could guide clinicians in the application of strategies aimed at suicide prevention